Small Lie algebras in the Verlinde category

Abstract

This paper studies simple Lie algebras in the Verlinde category, with canonical fundamental group action, using combinatorial methods. We give an exhaustive list of such Lie algebras which either have length at most 3, or appear as a subalgebra of the restriction of the Lie algebra of a simple algebraic group along a principal morphism. The results and exceptions answer several questions and conjectures regarding Verlinde categories of algebraic groups and their Lie algebras.

Disclosure

“The large language model GPT-5.6 Sol was used for writing computer programs, finding references, and proofreading. All material in this paper was written by the author. 1. SL2 combinatorics Let us first establish combinatorial form”

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Classification

Code generation, completion, or debugging

Multiplier

2

Verified

2026-08-23T05:08:58.213842Z

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